PPT-Improved Approximation for the Directed Spanner Problem

Grigory Yaroslavtsev Penn State ATampT Labs Research intern Joint work with Berman PSU Bhattacharyya MIT Makarychev IBM Raskhodnikova PSU Directed Spanner Problem. Approximation . Algorithms. II. How. to . find. a heavy . weight. . cut. in a . graph. The MAX CUT Problem. Given an . undirected. . graph. G=(V,E) with . edge. . weights. . w:E->R. , . divide. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs (intern). Based on a paper at . ICALP’11. , joint with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Alexander . Veniaminovich. IM. , . room. . 3. 44. Friday. 1. 7. :00. or. Saturday 14:30. Approximation. . algorithms. . 2. We will study. . NP. -. hard optimization problem. 3. What you should know. Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . By. - . James C. Corbett, Jeffrey Dean, Michael Epstein, Andrew . Fikes. , Christopher Frost, JJ Furman. Sanjay . Ghemawat. , . Andrey. . Gubarev. , Christopher . Heiser. , Peter . Hochschild. , Wilson Hsieh,. Lee-Ad Gottlieb. Graph spanners. A spanner for graph G is a . subgraph. H. H contains vertices, subset of edges of G. Some qualities of a spanner. Degree, diameter, . stretch, weight. Applications: networks, routing, TSP… . Piotr. Berman, . Sofya. . Raskhodnikova. , . Ge. . Ruan. Pennsylvania . State University. Graph Spanners . [Awerbuch85,Peleg Schäffer89]. A . subgraph. . H. of . G . is a . k. -spanner. . if for all pairs of vertices . Spanner of Directed Graphs. Kyomin. Jung. KAIST. 2009 . Combinatorics. Workshop. Joint work with . A. rnab. Bhattacharyya . MIT. . Elena . Grigorescu. . MIT. . . 1) . M. Hajiaghayi, . Khandekar. and K.. 2) . M. . Cygan. ,. K. 3) . R . Chitnis. , . M. Hajiaghayi. ,. K . 4) . M. Hajiaghayi, K and some students of M. Hajiaghayi. Optimal running times for exact solutions and approximated solutions. Problem. Yan Lu. 2011-04-26. Klaus Jansen SODA 2009. CPSC669 Term Project—Paper Reading. 1. Problem Definition. 2. Approximation Scheme. 2.1 Instances with similar capacities. 2.2 General cases . Outline. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. System. David F. Bacon et al. . Google, Inc. . Presenter: Che-Lin Huang. Overview. Motivation. Introduction to Spanner. Distributed . Query. Query Range . Extraction. Query . Restart. Common SQL . Dialect. How do weights affects approximation algorithms?. As usual there are no rules whatsoever.. However I will provide some interesting examples in which weights make a difference. I will try and say for every problem, why weights make a difference..